Abstract: High-dimensional interaction models have important applications in many scientific fields, especially in genetic research and medical studies. As in high-dimensional main-effect models, feature selection is unavoidable in high-dimensional interaction models. However, feature-selection methods for high-dimensional main-effect models cannot be applied directly to high-dimensional interaction models because of imbalanced spurious correlations between main-effect features and interaction features. Most studies on high-dimensional interaction models impose a so-called hierarchy principle, using various mechanisms. However, this approach is questionable, as we argue here. We propose a sequential-interaction group-selection (SIGS) method based on the principle of correlation search. The SIGS method avoids the drawbacks of imposing the hierarchy principle and has desirable properties. The selection consistency of the SIGS method is established. Simulation studies demonstrate that the SIGS method outperforms methods that impose the hierarchy principle.

Key words and phrases: Feature selection, group search, hierarchy principle, high-dimensional interaction models, principle of correlation search, sequential procedure.